Consider the set of 3CNF propositions over the variables {p, q,r} for which no clause appears…

 

Consider the set of 3CNF propositions over the variables {p, q,r} for which no clause appears more than once. (Exercises 3.102–3.104 turn out to be boring without the restriction of no repeated clauses; we could repeat the same clause as many times as we please: (p ∨ q ∨ r) ∧ (p ∨ q ∨ r) ∧ (p ∨ q ∨ r) · · · .) Two clauses that contain precisely the same literals (in any order) do not count as distinct. (But recall that a single clause can contain a variable in both negated and unnegated form.) In terms of the number of clauses, what’s the largest 3-variable distinct-clause 3CNF proposition . . .

1. . . at all (with no further restrictions)?

2. . . . that’s a tautology?

3. . . . that’s satisfiable?

Exercises 3.102–3.104

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